Workshops

Estimation and Control Problems in Adaptive Optics

Overview

Adaptive optics is the technology of sensing, estimating, and correcting the distortions induced in beams of light as they propagate through turbulent media. Applications include ground-based astronomical imaging and spectroscopy, laser power beaming through the atmosphere, and imaging the retina of the human eye. The fundamental components of an adaptive optical (AO) system are a wavefront sensor to measure the distortions in the optical beam, a wavefront corrector to compensate these errors, and an estimation and control algorithm to derive the control signals from the distortion measurements. The current generation of AO systems for ground-based imaging apply corrections to a few hundred to about one thousand degrees of freedom at update rates between a few hundred and a few thousands samples/second, using linear control algorithms that are implemented as explicit matrix multiplies. Proposed future systems could increase the number of degrees of freedom by a factor between ten and one hundred, with additional complexities introduced via the use of multiple wavefront sensors and correctors. More efficient control algorithms must be developed for these larger and more sophisticated systems, together with the theory to evaluate and optimize their performance.

Encouraging initial results are now being obtained in a variety of computational experiments investigating the simpler problem of estimating the instantaneous value of the phase disturbance from a single wavefront sensor snapshot. Some of the estimation algorithms under investigation include spatial filtering via fast Fourier transforms, sparse matrix methods, conjugate gradients with multi-grid or circulant preconditioning, and “hybrid” combinations of these methods. These methods have computational complexity between O(n log n) and O(n 3/2), as opposed to O(n3) to compute, and O(n2) to apply, conventional matrix multiply algorithms. But more work is necessary to optimize, understand, extend, and eventually implement these new approaches. Some of this work includes:

Developing a theoretical understanding of the observed convergence properties of these algorithms, and applying this theory to further research.

Progressing from wavefront estimation to wavefront control. This involves issues including stability, evaluating and optimizing the performance of the algorithm in closed loop, and perhaps developing adaptive control algorithms that adjust themselves in real time with changing conditions. None of the approaches currently used for comparatively low order AO systems appear scalable to the very high order systems of the future.

Developing a theoretical understanding of the observed performance of AO systems as a function of the wavefront sensing and correcting parameters. Once again, the methods presently applied to existing low-order systems are not scalable.

Developing entirely new control algorithms for adaptive optics under conditions of extreme wavefront distortions, where the current linear algorithms must be replaced by iterative, nonlinear methods involving projections onto convex sets.

We believe that this meeting can lead to a new synthesis of ideas and numerous valuable collaborations and initiatives, towards a goal of developing advanced control algorithms that will enable an entirely new generation of AO for future giant telescopes.